A sophist was a man who made his living by teaching things that would be useful to them and are not taught in regular curriculum. As there was no public provision for such education, the Sophists taught only to those who had private means. This tended to give them a certain class bias which was increased by political circumstances of the time.
In Athenian democracy, judges and most executive officers were chosen by lot and served for short periods. They were thus average citizens with their characteristic prejudices and lack of professionalism. The plaintiff and defendant or prosecutor and accused appeared in person, not through professional lawyers. Naturally, success and failure depended largely on oratorical skill in appealing to popular prejudices. Although a man had to deliver his own speech, he could hire an expert to write the speech for him, or, as many, preferred, he could pay for instruction in the arts required for success in the law courts. These arts the Sophists were supposed to teach. They taught the art of arguing, and as much knowledge as would help in this art. Broadly speaking, they were prepared, like modern lawyers, to show how to argue for or against any opinion and were not concerned to advocate conclusion of their own. Those, to whom philosophy was closely bound to religion, were naturally shocked; to them, the sophists appeared frivolous and immoral. The sophists were prepared to follow an argument wherever it might lead them. Often it led to skepticism. One of them, Gorgias, maintained that nothing exists; that if anything exists; and to be knowable by any one man, he could never communicate it to others.
Protagoras was most prominent amongst the sophists. Protagoras was born about 500 B.C; at Abdera in Thrace, the city from which Democritus came. He twice visited Athens. His second visit to Athens is described somewhat satirically in Plato’s Protagoras, and his doctrines are discussed seriously in Theaetetus. He is chiefly noted for his doctrine that “Man is measure of all things, of things that are that they are, and of things that are not that they are not.” This is interpreted as meaning that each man is the measure of all things and that when men differ there is no objective truth in virtue of which one is right and other is wrong. The doctrine is essentially skeptical and is presumably based on deceitfulness of the senses.
Russel quotes Plato, in the Theaetetus, to explain Protagoras. One opinion can be better than other but not necessarily truer. For e.g. when a man has jaundice everything looks yellower to him. There is no sense in saying that things are not really yellow, but the color they look to a healthy man, one can say, however that since health is better than sickness, the opinion of man in health is better than that of man who has jaundice. This point of view is akin to Pragmatism.